The Retirement Income Equation
Understanding how to arrive at a target replacement rate
By Marlena I. Lee, PhD
Vice President
Dimensional Fund Advisors
June 2013
THE RETIREMENT INCOME EQUATION
INTRODUCTION
How much retirement income is enough? The answer depends on a household’s unique needs. If we define
successful retirement planning as the ability to maintain one’s preretirement standard of living, common
advice recommends that households target 75% to 85% of preretirement income. However, while this can
be a useful starting point, understanding how to arrive at a target replacement rate can be helpful for future
retirees and plan sponsors alike.
Those engaged in retirement planning should understand what is typical for households with similar
characteristics. This is an improvement over one-size-fits-all financial advice. This article also provides
a roadmap for how one might adjust the recommended replacement rate to fit a unique situation.
For plan sponsors, understanding what replacement rate is appropriate for participants is critical
in assessing a plan’s adequacy. Benchmarking retirement plans without controlling for participant
characteristics might lead to faulty conclusions about retirement readiness.
The purpose of this study is to provide a framework for determining a target replacement rate that will
allow a household to maintain its preretirement standard of living. The study considers actual spending
patterns of thousands of US households while taking into account uncertainty in investment outcomes
and career paths. The results indicate that replacement rates can vary widely, from less than 60% for highly
compensated employees to over 80% for low-wage earners. By comparing the prescribed results to actual
behavior, we can draw conclusions about the feasibility of DC plans as a primary source of retirement
income for future retirees.
THE FRAMEWORK
Common sense tells us most people need to replace less than 100% of their gross preretirement income
in retirement. While working, income goes to one of three things: taxes, savings, or spending. However,
retirees typically pay fewer taxes and no longer need to save for retirement. In a simple example, if a
household saved 10% for retirement and had an effective tax rate of 10% while working and 0% when
retired, an 80% replacement rate would be required in order to achieve the same level of spending enjoyed
before retirement.
Should people target the same level of spending? A wealth of academic research suggests the answer is no.
Economic theory suggests people should target the same standard of living; however, this may not mean
the same thing as targeting a dollar level of spending. A simple example would be a homeowner whose
mortgage is paid off before retirement. Since the homeowner lives in the same house during retirement,
there is no change in standard of living, but out-of-pocket housing expenses will decline. In such cases,
incorporating a decline in spending might make sense for some households.
Returning to our previous example, suppose the homeowner decides the preretirement standard of living
can be sustained even if spending declines by 10%. Since 80% of gross preretirement income was being
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DIMENSIONAL FUND ADVISORS
spent, the change represents a decline of 8% of gross income (10% of 80%). Now the target replacement rate
is 72% (100% less 10% for taxes, 10% for saving, and 8% for spending adjustment). Figure 1 illustrates the
framework used in this study to compute replacement rates. By estimating effective tax rates, spending needs
to maintain a standard of living, and the appropriate savings rate needed to support that level of spending, we
can solve for target replacement rates.
Figure 1. REPLACEMENT RATES SHOULD BE LESS THAN 100%
Taxes
Constant Dollars
2
Savings
Pension income
+
Income from personal savings
Spending
Social Security
Working Years
Retirement
SPENDING NEEDS
For over four decades, academics have known that spending is hump-shaped over the life cycle (Thurow
1969). Figure 2 displays median nondurable spending from age 25 to 90 for a sample of 69,827 households.
Spending peaks around age 45 before declining. Many explanations for this spending profile have been
proposed, including changes in family size, borrowing constraints, savings behavior, and leisure time, but
we need to rule out insufficient financial resources as the primary reason. Otherwise, it does not make
sense to incorporate this hump-shaped pattern into retirement plans. It is also important to understand
whether all types of households should anticipate these spending declines, or whether the effect is
concentrated among a subset of households.
Breaking down nondurable spending into categories suggests the decline is not due to poor planning
(Aguiar and Hurst 2008). Figure 3 shows median spending around retirement on discretionary items such
as trips and vacations, entertainment events, hobbies, and charity. At all income quartiles, we observe that
median spending increases for these nonessential items. If the spending decline observed over the life cycle
was due to insufficient financial resources, one would expect discretionary spending to take the biggest hit.
Another category that households tend to spend more on with age is medical care. As shown in Figure 4,
out-of-pocket expenses on insurance premiums, medications, doctor visits, hospital stays, medical supplies,
and nursing home care increase for all income groups as people get older.
THE RETIREMENT INCOME EQUATION
Figure 2. MEDIAN NONDURABLE SPENDING OVER THE LIFE CYCLE 1
50
45
2010 Dollars (Thousands)
40
35
30
25
20
15
10
5
0
25
30
35
40
45
50
55
60
65
70
75
80
85
90
Sources: BLS, National Bureau of Economic Research.
Figure 3. MEDIAN DISCRETIONARY SPENDING BY INCOME QUARTILE 2
Age 56–60
Age 61–65
Age 66–70
Age 71–75
Age 76–80
12,000
2010 Dollars
10,000
8,000
6,000
4,000
2,000
0
< 25th
Source: RAND Corporation.
25th–50th
50th–75th
> 75th
Income Percentile
1. Spending data for 69,827 households is from the Bureau of Labor Statistics Consumer Expenditure Survey; Family-Level
Extracts, 1980: 1–2003:2, compiled by Ed Harris and John Sabelhaus and provided by the National Bureau of Economic
Research. Values are converted to real 2010 dollars using CPI-U from the Bureau of Labor Statistics.
2. Median discretionary expenses by income quartiles. Income quartiles are based on the average of the three highest
observations of total household income. The 25th, 50th, and 75th percentiles of income are $25,327, $49,755, and
$93,980, respectively. Sample contains 12,625 observations. Source: RAND HRS, waves 1–9 and HRS CAMS 2001–2009.
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Figure 4. MEDIAN OUT-OF-POCKET MEDICAL CARE SPENDING 3
Age 56–60
Age 61–65
Age 66–70
Age 71–75
Age 76–80
6,000
5,000
2010 Dollars
4
4,000
3,000
2,000
1,000
0
< 25th pct
Source: RAND Corporation.
25th–50th
50th–75th
> 75th
Income Percentile
A few factors explain the overall decline in spending, despite observed increases in discretionary and
medical spending. For example, households tend to spend less on food in retirement. Retirees have
more time to prepare their meals at home and shop around for better prices. Aguiar and Hurst (2007)
find older households dedicate more time to shopping, and as a result, pay lower prices for the same
products. Households also tend to spend less on work-related items in retirement, such as clothing and
transportation. Among homeowners, we observe a large reduction in housing expenses because mortgages
are typically paid off by retirement. Within this sample, the net effect on total nondurable spending has
been a robust decline of about 10%–16% for households with income above the median. For households
with income below the median, there is not a robust change in spending (see Figure 5). In this sample, the
typical household with an annual income of $50,000 or more reduced spending by about 10% or more.
Households with income below this threshold held spending roughly constant.
These findings are remarkably consistent with the planning behavior reported in a survey of 1,000 plan
participants conducted by Dimensional Fund Advisors and the Boston Research Group. Relative to current
spending, 45% of participants plan on spending less in retirement. Only 11% of participants plan to spend
more, with the remainder expecting to keep spending about the same. There is a big range in individual
outcomes, so people must consider their unique needs and how they might differ from the “typical” household.
Future retirees must also consider how budget shares might change in the future. For example, the budget
share of medical care has risen over time, and many predict that it will continue to rise. Thus, the spending
patterns of households in the past may not adequately reflect the challenges of retirees in the future.
3. The figure shows median out-of-pocket medical expenses by income quartiles. Sample contains 11,995 observations.
Source: RAND HRS, waves 1–9 and HRS CAMS 2001–2009.
THE RETIREMENT INCOME EQUATION
Figure 5. MEDIAN NONDURABLE SPENDING BY INCOME QUARTILE 4
Age 56–60
Age 61–65
Age 66–70
Age 71–75
Age 76–80
70,000
60,000
2010 Dollars
50,000
40,000
30,000
20,000
10,000
0
< 25th
Source: RAND Corporation.
25th–50th
50th–75th
> 75th
Income Percentile
SAVINGS RATES
Determining spending needs in retirement is one step in determining an appropriate replacement rate.
The next step is to determine what savings rate is consistent with achieving those spending goals. How
much savings is needed is a very difficult question. A partial list of considerations would include risk
tolerance, target retirement age, current savings, perceived health status, and predicted career path. To look
at all combinations of these relevant factors is outside the scope of this article. Instead, we provide some
simulation evidence around a general base case.
We simulate income and portfolio paths of 10,000 households. The working years are age 25 to 65, and full
retirement occurs at 66. Final preretirement income matches the actual income distribution of households
age 60 to 64 in 2009.5 Pay raises and portfolio outcomes are jointly drawn from historical distributions
of changes in real per capita income and real stock and bond returns over the period from 1930 to 2010.6
Each year, the households save a fixed fraction of their gross income in a Roth retirement vehicle. The
portfolio is invested in stocks and bonds, with the percent invested in stocks equaling 100% – age.
We assume households with below (above) median final income want to replace 100% (90%) of preretirement
spending, where preretirement spending equals gross income—less savings, federal income taxes, and
FICA taxes—estimated using current tax laws and standard deductions. A household’s spending is partially
funded by Social Security, but any shortfall is financed using personal savings. Figure 6 on the following
page shows the savings rates needed to achieve this spending level (or more) with 75%–90% probability,
assuming the price of a $1 real annuity is $20. Even with a Social Security replacement rate of 59% for the
4. The figure shows median nondurable spending by income quartiles. Sample contains 5,356 observations.
Source: RAND HRS, waves 1–9 and HRS CAMS 2001–2009.
5. Source: US Census Bureau. 2010 Current Population Survey, Annual Social and Economic Supplement.
6. Real changes in per capita income obtained from Bureau of Economic Analysis. National Income and Product Accounts
tables. The assumption that the household does not defer taxes allows me to complete the analysis without having to
make predictions about future tax rates.
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lowest income quartile, savings must be about 10% to maintain at least the same level of preretirement
spending in about 85% of the simulations. For households with annual income exceeding $25,870, a savings
rate in the low teens is required to maintain spending levels with high probability.
Required savings rates might be lower if a household is willing to take more risk or target a lower
spending level. Alternatively, savings rates might need to be higher if a person started saving later, did
not consistently save, is more risk averse, or would like to target higher levels of retirement spending.
Figure 6. SIMULATION EVIDENCE
Percentile of Preretirement Income
< 25th
25th–50th
50th–75th
> 75th
Preretirement income range
< $25,870
< $49,941
< $86,882
> $86,882
Median effective tax rate
8%
14%
18%
21%
Savings rate
9%–11%
13%–15%
12%–14%
13%–16%
Spending adjustment
0%
0%
10%
10%
Total
81%–83%
71%–73%
61%–63%
57%–59%
Social Security
59%
38%
31%
21%
Replacement Rate
PUTTING IT ALL TOGETHER
Replacement rates can differ substantially across households depending on individual retirement goals,
tax rates, and accumulated savings. Using preretirement income as a sorting variable, we obtain income
replacement rates that range from 58% for highly compensated employees to about 82% for low-wage
earners. Replacement rates decline as income increases for a number of reasons:
• High-income households tend to reduce spending as they transition into retirement.
• Tax rates are higher for high-income households.
• Social Security replacement rates are lower, thus necessitating higher savings rates.
Households that consistently save throughout the working years need to target savings rates of 10%
to 15%—which is not that far off from observed behavior. Among active DC participants in the 2007
Survey of Consumer Finances, median total contribution rates (including both employee and employer
contributions) range from 8% to 12%, depending on income level.
Of course, many participants do not save as early and as consistently as in the previous simulations. This
fact leaves room for improvement, perhaps through plan design and education. The current trends toward
auto-enrollment and auto-escalation are promising, but we believe plan sponsors should remain vigilant
about improving their plans. As we look to the next generation of retirement plans, it’s important to move
the paradigm from savings to consumption planning.
THE RETIREMENT INCOME EQUATION
REFERENCES
Aguiar, Mark, and Erik Hurst. “Life Cycle Prices and Production.” American Economic Review 97 (2007):
1533–59.
Aguiar, Mark, and Erik Hurst. “Deconstructing Life Cycle Expenditure.” NBER working paper series
13893 (2008).
Thurow, Lester. “The optimum lifetime distribution of consumption expenditures.” American Economic
Review 59 (1969): 282–297.
ABOUT THE AUTHOR
As a vice president on Dimensional’s Research team, Marlena Lee conducts research
in asset pricing and macroeconomics. She shares the results through published research
and in presentations to institutions and financial advisors who work with Dimensional.
Prior to joining Dimensional, Marlena gained experience explaining complex financial
concepts as a teaching assistant for several professors, including Professor Eugene Fama.
She has also worked as an economic consultant on antitrust litigation cases and as a
research assistant at the Manhattan Institute of Policy Research.
Marlena earned her PhD in finance from the University of Chicago Booth School of Business. She also
holds an MBA from the Booth School of Business, and an MS in agricultural and resource economics
and a BS in managerial economics from the University of California, Davis.
Dimensional Fund Advisors LP is an investment advisor registered with the Securities and Exchange
Commission. The projections or other information generated by Monte Carlo analysis tools regarding the
likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results,
and are not guarantees of future results. Results may vary with each use and over time. These hypothetical
returns are used for discussion purposes only and are not intended to represent, and should not be
construed to represent, predictions of future rates of return. Actual returns may vary significantly.
Past performance is no guarantee of future results.
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